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Search: id:A070160
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| A070160 |
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Nonprime numbers n such that q=phi[n]/(sigma[n]-n-1) is an integer. |
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2
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| 4, 9, 15, 25, 35, 49, 95, 119, 121, 143, 169, 209, 287, 289, 319, 323, 361, 377, 527, 529, 559, 779, 841, 899, 903, 923, 961, 989, 1007, 1189, 1199, 1343, 1349, 1369, 1681, 1763, 1849, 1919, 2159, 2209, 2507, 2759, 2809, 2911, 3239, 3481, 3599, 3721
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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EulerPhi value divided by Chowla function gives integer.
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FORMULA
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q=A000010(n)/A048050(n) is integer.
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EXAMPLE
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n=15:q=8/8=1; n=101:q=100/1=100. While integer quotient, q1=Chowla[n]/Phi[n] gives only 5 nonprime solutions below 20000000 (see A070037), here, the integer reciprocals, q=Phi[n]/Chowla[n] obtained with prime squares and with other composites. If n=p^2, q=p(p-1)/p = p-1. So for prime squares, the quotients give A006093. This sequence is union of primes and A070161.
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MATHEMATICA
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Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n-1); If[IntegerQ[s], Print[n]], {n, 2, 100000}]
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CROSSREFS
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Cf. A000010, A001065, A000203, A020492, A068418, A062972, A055940, A070159, A070037, A070161.
Sequence in context: A050530 A102084 A030664 this_sequence A056928 A122964 A070447
Adjacent sequences: A070157 A070158 A070159 this_sequence A070161 A070162 A070163
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 26 2002
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